I don't think it is that hard a question to answer.
1 Corinthians 1:11-12 KJV
For it hath been declared unto me of you, my brethren, by them which are of the house of C

e, that there are contentions among you. [12] Now this I say, that every one of you saith, I am of Paul; and I of Apollos; and I of Cephas; and I of Christ.
The Corinthians were decided. They were bickering by saying, "well , I follow Paul and what he says!". Another would say,"I follow Apollo's!". Others would say, " Bah! I follow no man: I follow Christ!". Same with Peter...
Paul was disgusted with this attitude. He said in Chapter 3:6 that he planted, Apollo's watered but God gave increase. He also said that Apollo's and he were on the same page.
1 Corinthians 1:13-17 KJV
Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul?
He is upset at the division as both he and Apollo's are on the same page ("are one" as he put it in ch 3) and they are both preaching Christ. So there shouldn't be any divisions.
[14] I thank God that I baptized none of you, but Crispus and Gaius;
[15]
Lest any should say that I had baptized in mine own name.
[16] And I baptized also the household of Stephanas: besides, I know not whether I baptized any other.
[17] For Christ sent me not to baptize, but to preach the gospel: not with wisdom of words, lest the cross of Christ should be made of none effect.
Let us realize that he did actually baptize (and the context is in water)! He gave two names and the name of a household. So while he did do it, God didn't send him for that purpose.
So why was he glad that he didn't baptize any of them? Because they were being foolish with their divisions. The was Team Paul, Team Apollo's, Team Peter and Team Jesus and apparently they took it seriously. Paul didn't like that there was a "Team Paul" either. He's happy he didn't baptize because they would've used the "baptism by Paul" as some sort of authentication against other Christian's.
In short, he was dealing with very immature Christian's and he didn't want them thinking he was the object of worship (more or less being the point).
Now, a few other things about this:
1. That doesn't mean they weren't baptized in water at all. Paul (like Jesus) may have had others do it.
2. Though that MAY be the case, it is reasonable to point out that he didn't seem to have strong feelings for it. He did it a few times, but he doesn't come across that it is that vital.